Unit 1: Preview and Review
While your first course in calculus can strike you as something new to learn, it is not comparable to learning a foreign language where everything seems different. Calculus still depends on most of the things you learned in algebra, and the true genius of Isaac Newton was to realize that he could get answers for this something new by relying on simple and known things like graphs, geometry, and algebra. There is a need to review those concepts in this unit, where a graph can reinforce the adage that a picture is worth one thousand words. This unit starts right off with one of the most important steps in mastering problem solving: Have a clear and precise statement of what the problem really is about.
Completing this unit should take you approximately 6 hours.
1.1: Preview of Calculus
This section reviews how algebra will help you in the study of calculus. In this unit, you will review two main topics: finding the slope of tangent lines from a graph and finding the area of an irregular shape.
1.2: Lines in the Plane
In this section, you will begin the study of calculus. It is important to understand the properties and equations of straight lines since they set the tone for differential calculus.
1.3: Functions and Their Graphs
Functions and their graphs are essential concepts in calculus. You will learn about the behavior of functions, which are ideas that you can apply to many fields.
1.4: Combinations of Functions
In this section, you will continue to learn about functions. You will take it a step further by combining basic functions to solve more complicated problems in calculus.
1.5: Mathematical Language
This section is very important in learning calculus. It is important to understand some common mathematical phrases to be able to understand the concepts being discussed.